Solve for x, rounding to the nearest hundredth. 2^((x)/(5))=12 Answer:

Write Equation: Write down the equation that needs to be solved. We have the equation 2^(x/5) = 12.Take Natural Logarithm: Take the natural logarithm (ln) of both sides to remove the exponent on the left side. ln(2^(x/5)) = ln(12)Use Logarithmic Property: Use the logarithmic property that ln(a^b) = b*ln(a) to simplify the left side. (x/5)*ln(2) = ln(12)Solve for x: Solve for x by multiplying both sides by 5 and then dividing by ln(2). x = (5*ln(12)) / ln(2)Calculate x: Calculate the value of x using a calculator. x ≈ (5*2.48490665) / 0.69314718 x ≈ 12.42453325 / 0.69314718 x ≈ 17.925416Round to Nearest Hundredth: Round the value of x to the nearest hundredth. x ≈ 17.93

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Solve for
x, rounding to the nearest hundredth.

2^((x)/(5))=12
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $2^{\frac{x}{5}}=12$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

2^{\frac{x}{5}}=12

\newline

Answer:

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $2^{(x/5)} = 12$ .
Take Natural Logarithm: Take the natural logarithm ( $\ln$ ) of both sides to remove the exponent on the left side. $\newline$ $\ln(2^{x/5}) = \ln(12)$
Use Logarithmic Property: Use the logarithmic property that $\ln(a^b) = b\cdot\ln(a)$ to simplify the left side. $\frac{x}{5}\cdot\ln(2) = \ln(12)$
Solve for x: Solve for x by multiplying both sides by $5$ and then dividing by $\ln(2)$ . $x = \frac{5 \cdot \ln(12)}{\ln(2)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x \approx (5 \times 2.48490665) / 0.69314718$ $\newline$ $x \approx 12.42453325 / 0.69314718$ $\newline$ $x \approx 17.925416$
Round to Nearest Hundredth: Round the value of $x$ to the nearest hundredth. $x \approx 17.93$